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This paper describes an approach for augmenting a linear controller design with a neural-network-based adap- tive element. The basic approach involves formulating an architecture for which the associated error equations have a form suitable for applying existing results for adaptive output feedback control of nonlinear systems. The approach is applicable to non-affine, nonlinear systems with both parametric uncertainties and unmodelled dy- namics. The effect of actuator limits are treated using control hedging. The approach is particularly well suited for control of flexible systems subject to limits in control authority. Its effectiveness is tested on a laboratory experiment consisting of a three-disk torsional pendulum system, including control voltage saturation and stiction. HIS paper describes an approach for augmenting a linear con- troller design with a neural-network (NN)-based adaptive el- ement. Previous adaptive output feedback control approaches have been applied within a control architecture that uses an inverting type of controller for the nonadaptive portion of the control system. 1,2 Considering that the vast majority of controllers are locally linear controllers, it would be highly desirable to retrofit such systems with an adaptive element, rather than to replace them with an inverting controller. In particular, within the aircraft and automobile industries there is a legacy of experience with existing control system archi- tectures, and these industries would much prefer to augment their controllers with an adaptive process, rather than replace them with a totally new architecture. This is particularly the case in applications calling for control of flexible systems. Several attempts to develop a method for adding an adaptive ele- ment to an existing controller architecture have recently appeared in the literature. 3−9 The methods 3−6 are restricted to state feedback and impose restrictive conditions with respect to properties of the reg- ulated variable and the manner in which the uncertainty affects the plant. For example, they might require that the regulated output has full relative degree (meaning that the number of times the regulated variable must be differentiated before the control appears equals the number of state variables needed to describe the plant dynamics) or that the plant uncertainty is matched (meaning that the uncertainty enters the plant dynamics in the same manner as the control). Be- cause the methods 3−7 are based on matching the state response of an idealized model with that of the true plant, they cannot be applied to a system of higher order than the model used in the design process. As a consequence, they are not robust to the unmodeled dynam- ics. The methods in Refs. 8 and 9 use an adaptive technique called input error method 10 for reconfigurable flight control. It requires, however, that the open-loop system is stable. State feedback is very restrictive, and flexible systems provide a good example in which a state feedback approach is not useful. The controller architecture proposed in this paper relies on re- cent developments in the area of nonlinear adaptive output feedback

Augmenting Adaptive Approach to Control of Flexible Systems